Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<iostream>
#include<algorithm>
#include<cstdio>
using namespace std;
int main() {
	int N, line[1000];
	cin >> N;
	for (int i = 0; i < N; ++i) {
		cin >> line[i];
	}
	sort(line, line + N);
	double ans = 0;
	for (int i = 1; i < N - 2; ++i) {
		ans = max((double)(line[N - 1] + line[N - 2]) / (line[i] - line[i - 1]), ans);
	}
	ans = max((double)(line[N - 1] + line[N - 4]) / (line[N - 2] - line[N - 3]), ans);
	ans = max((double)(line[N - 3] + line[N - 4]) / (line[N - 1] - line[N - 2]), ans);
	printf("%.6lf\n", ans);
	return 0;
}